Method and apparatus for resolving transducer ambiguity

ABSTRACT

A METHOD AND APPARATUS FOR RESOLVING AMBIGUITY IN THE OUTPUT OF CIRCULAR FUNCTION TRANSDUCERS BY GENERATING A SIGNAL IN QUADRATURE WITH THE ORIGINAL TRANSDUCER OUTPUT IS DISCLOSED.

Feb. 16, 1971 J. w. CAMPBELL Er AL METHOD AND APPARATUS FOR RESOLVINGTRANSDUCER AMBIGUITY Filed Nov. 9, 1967 5 Sheets-Sheet 2 PHOTOCELLPlEZO-ELECTRlC/ CRYSTAL 9 DETECTOR LASER 3/ DISPLACEMENT (Y:

f DEVICE l4 II I2 23 AUDIO OSCILLATOR BAND PAss rgg g i Low PASSQUADRATURE F'LTER AMPLIFIER FILTER Low PAss C RIGINAL FILTER 7 A r L .Jx

. INVENTORS JAMES w. CAMPBELL BY VIRGIL ERBERT WWW I ATTORNEYS Feb. 16,1971 J. w. CAMPBELL EI'AL 3,563,664

METHOD AND APPARATUS FOR RESOLVING TRANSDUCER AMBIGUITY Filed Nov. 9,1967 5 Sheets-Sheet 5 E A Fmms LOW PASS FILTERS BAND PASS FILTERS l I I1' I I I I I I i l I I I I 1 l I I 1 I I I o I i I 1 I I 7 QUADRATURETIME ORIGINAL A B F IG...@ C

QUADRATURE WAVE FORM 63 64 SHAPER I 62 DHRECTIONAL UP DOWN LOGIC COUNTER57 IGINAL WAVE FORM SHAPER RECORDER ANGLE RESOLVER 7B INVENTORS F 7JAMES W. CAMPBELL By VIRGIL ERBERT ATTORNEYS United States Patent METHODAND APPARATUS FOR RESOLVING TRANSDUCER AMBIGUITY James W. Campbell, 1205Madeira SE., Albuquerque, N. Mex. 87108, and Virgil Erbert, Albuquerque,N. Mex.; said Erbert assiguor to said Campbell Filed Nov. 9, 1967, Ser.No. 681,686 Int. Cl. G01b 9/02; H01s 3/00 US. Cl. 356-106 10 ClaimsABSTRACT OF THE DISCLOSURE A method and apparatus for resolvingambiguity in the output of circular function transducers by generating asignal in quadrature with the original transducer output is disclosed.

The invention described herein was made in the course of, or under, acontract with the United States Atomic Energy Commission.

This invention relates to a new and improved method and apparatus forgenerating a quadrature signal in the output of circular functiontransducers in order to resolve ambiguity in the transducer output.

A circular function transducer is an energy conversion device whoseoutput is a substantially sinusoidal function of the input to thedevice. The sinusoidal nature of the output from such a transducercreates an ambiguity as to which of many possible input values producedany one output value. In particular, the output of such a deviceprovides no information as to the direction of change of the input.

Circular function transducers are useful in certain areas of measurementwhere the input to the transducer corresponds to variation in aparameter to be measured, the periodic transducer output therebyproviding a measurement of the variation. One of the most widely usedcircular function transducers are optical interferometers which produceintensity changes of light which are substantially sinusoidal functionsof variations in the optical path length traveled by the interferometerlight beams. Microwave interferometers are similarly circular functiontransducers. Because the optical path length depends upon the distanceand the refractive indexof the medium through which the beam travels,such transducers can be used to measure distances, densities, refractiveindices, etc. with great accuracy.

Although it is possible to count the sinusoidal intensity changes,fringes, or cycles in the output of such interferometers, the outputprovides no information as to whether the input is increasing ordecreasing. Thus, eX traneous vibrations or variations in the opticalpath length may distort counting at the output without detection.Furhermore, within any one cycle, the output provides no information asto which side of a cycle a particular value belongs. Such directionalinformation is at best extremely difiicult to ascertain.

In the past, ambiguity in interferometers has been resolved with aquadrature system by construction in effect two interferometers withsubstantial duplication of equipment which simultaneously measure theoptical path length of interest. The sinusoidal output of the secondinterferometer is mechanically phase shifted 90 from the sinusoidaloutput of the first interferometer. The two signals together provide thedirectional information necessary to resolve ambiguities in the outputof the first interferometer. Thus, the sinusoidal output of the secondinterferometer will lead the sinusoidal output of the firstinterferometer by 90 for a variation in the parameter to be measured inone direction and will lag by for a change in the parameter in theopposite direction. This conventional quadrature technique requires anindependent and stable light source in order to provide the twodifferent intensity interferometer beams. The two outputs (original andquadrature) have unique pair of values for every input over a range ofone cycle.

The conventional quadrature system is inapplicable to the laser feedbackinterferometer (LFI) which can produce only a single intensity beam. Inthe laser feedback interferometer, the light intensity of the laser isdetermined by the amount of feedback of its own light from an externalreflector. The net inphase contribution of the reflected light into thelaser determines the output of the transducer. Thus, an additionalfeedback path as would be required in the conventional twointerferometer quadrature system, would combine with other feedbackpaths to result in a single feedback function producing a single phaseoscillation at the output of the laser. It is therefore, impossible toobtain the two intensity beams necessary for the conventional quadraturetechnique. Before the present invention there was no known technique forobtaining quadrature information from the output of the LFI.

Other circular function transducers such as the e ectrooptic Kerr Cellpolarimeter also require some quadrature technique in order to resolveambiguity.

It is an object of the present invention to provide a simplified anduniversally applicable method for obtaining quadrature information fromcircular function transducers by utilizing a single input and output ofthe transducer to obtain directional information in the output as tovariations in the input. The invention thereby avoids substantialduplication of equipment and additionally may be carried out withcommercially available electronic components.

In order to accomplish these results, the present invention contemplatesmodulating the input to a circular function transducer produced by avariation in the parameter to be measured. At the output of thetransducer, the original output frequency component attributable to thevariation in the parameter to be measured is separated from themodulating frequency component which contains the quadratureinformation. The invention further contemplates demodulating themodulating frequency component of the transducer output to obtain asignal in quadrature with the original output attributable to avariation in the parameter to be measured. The technique is thusapplicable to the laser feedback interferometer where only the one laserbeam intensity is available, and to other circular function transducerssuch as optical interferometers, polarimeters, spectrometers,photometers, electrometers, magnetometers and the laser ring gyro.

Another aspect of my invention contemplates applying this technique toprovide a means for compensating interferometers for changes in theambient atmosphere. In effect, two laser feedback interferometers arethereby provided from a single intensity laser source.

Other objects and advantages of the present invention will becomeapparent upon reading the following specifi cation and referring to theaccompanying drawings in which corresponding numerals representcorresponding parts in each of the several views.

In the drawings:

FIG. 1 is a block diagram of the apparatus and method for producingquadrature information in circular function transducers;

FIG. 2 is a graph illustrating the mathematical relationship between theoriginal transducer output and the modulating signal;

FIG. 3 is a block diagram of the apparatus and method of the presentinvention as applied to a laser feedback interferometer;

FIG. 4 is a diagrammatical illustration showing one form of displacementdevice or carriage for use with the present invention;

FIG. 5 is a graph showing the characteristics of the low pass filtersand band pass filters illustrated in FIG. 3;

FIG. 6 is a graph of experimental results showing the relationshipbetween the original signal and the quadrature signal from the apparatusand method illustrated in FIG. 3;

FIG. 7 is a block diagram of data processing apparatus and method forthe output signals from the apparatus and method illustrated in FIG. 3;

FIG. 8 is a block diagram showing the apparatus and method foradditionally obtaining compensation information as applied to a laserfeedback interferometer;

FIG. 9 is a graph showing the limiting characteristics of the low passfilters and band pass filters illustrated in FIG. 8; and

FIG. 10 is a block diagram showing the data processing apparatus andmethod for the output signals from the apparatus and method illustratedin FIG. 8.

The embodiment of my invention illustrated in FIG. 1 is generallyapplicable to transducers to the type in which the input corresponds toa variation in a parameter to be measured and the output is asubstantially sinusoidal function of the input for uniform variations inthe input. The frequency of the sinusoidal output is proportional to therate of change of the parameter to be measured. Thus, as illustrated inFIG. 2, a uniform variation of the input, .r, along the horizontal axiscorresponding to a uniform variation in the parameter to be measuredproduces a sinusoidal output, F(x), defined by the following equationwherein X, A, n and 1) are constants of the particular transducer.

According to the present invention shown in FIG. I, this input 1 to thecircular transducer 2 corresponding to a variation in the parameter tobe measured is modulated by a small periodic perturbation of frequency fand amplitude Ax as illustrated in FIG. 2. Thus, for any particularvalues X of the input there will be a small variation about that pointin the output whose value is a function of the time t and the value xThe transducer input is modulated by a sinusoidal generator 3 and alinear transducer 4 which converts the signal to a perturbationcompatible with the input to the transducer, as illustrated in FIG. 1.

The output from the circular transducer thus becomes a function of boththe uniform variation of the input x, and the time t, i.e., F(x, t), andis defined by the following equation which is the classical phasemodulation equation of communication theory.

This expression can be expanded to the following more relevant form.

Ax T )cos mQvrf [Equation 3] The first two terms to the right of theequal sign are the same as Equation 1 with the factor A multiplied by aconstant Jo er) Ax ano X being constants and J being the Zero orderBessell function of the first kind. These two terms represent theoriginal circular transducer output corres onding to a variation in theparameter to be measured, with a frequency proportional to the rate ofchange in the parameter to be measured.

The third term is a component of frequency the modulating frequency. Theamplitude of the h frequency component is have a unique pair of valuesfor every input over a range of one cycle.

Accordingly, as illustrated in FIG. 1, the output from the circulartransducer 2 is coupled to a first low pass filter 5 and a band passfilter 6. The first lOW pass filter has an upper cutoff frequency atapproximately the maximum frequency f of the original output due to therate of change in the parameter to be measured. The output from thisfilter is the original signal. The band pass filter has a frequencyrange around the modulating frequency f in order to separate out thethird term in Equation No. 3 which contains the quadrature informationin its amplitude function. The band pass is approximately from h-f to f-l-f in order to preserve this quadrature information. The output fromthe band pass filter may then be demodulated to obtain a signalcorresponding to the amplitude function which is in quadrature with theoriginal signal.

The f frequency component is demodulated to obtain the amplitudefunction by coupling the output from the band pass filter to a mixer ormultiplier 7 which multiplies the f frequency component with the outputfrom the sinusoidal generator 3 which is the same frequency and the samephase. If a difference in phase exists between the signals beingmultiplied, a phase shifter must be connected between the sinusoidalgenerator 3 and mixer 7 to appropriately adjust the phase so that thetwo phases are the same. The frequency multiplier produces two signalsof approximately zero frequency and approximately twice the modulatingfrequency, h, each having the amplitude of the f frequency componentwhich is the function in quadrature with the original signal. A secondlow pass filter 8, with an upper cutoff frequency of approximately fselects the signal of approximately zero frequency and extracts theamplitude information to produce the quadrature signal.

Referring back to Equation No. 3,

in the second term in the third term and are constants for fixed Ax andX. Thus, Ax, the amplitude of the modulating signal must be chosen sothat is not a root of either the zero order or the first order Besselfunction. If that were so, either of the Bessel functions would be zero,thereby eliminating either the original output signal or the h frequencycomponent which includes the quadrature information. Advantageously Axmay be chosen so that the amplitudes of the two quadrature signals areequal as when Ax is approximately equal to .142X. Ax may also be chosenso that 21rA17 X is a root of higher order Bessel functions to therebyeliminate undesirable harmonics.

The fourth term in Equation No. 3 contains all the harmonics of theoriginal output frequency produced by the rate of change in theparameter to be measured and the modulating frequency f In order for thefrequency component f attributable to the rate of change in theparameter to be measured, the modulating frequency, f component andadditional harmonics at the output of the circular function transducermay be separable by simple filtering, it is apparent that f should be atleast twice as great as im. This is because the band pass filter 6 at fmust pass frequencies from f f to f l-i-f in order to preserve thequadrature information in the f frequency component as illustrated inFIG. 5. From a practical standpoint, f must be somewhat greater than Zfto allow for non-ideal cutoff characteristics of the filters. Theseconditions satisfied, each term in Equation 3 occurs in a differentfrequency range and is easily separated by simple filtering. Furtheranalysis of the Equation 3 reveals that in order to eliminateundesirable harmonics of f and h, the band pass filter should have anupper cutoff frequency no greater than three-halves h.

To summarize the requirements for simple filtering, the low pass filter5 should have the following characteristics:

f upper cutoff frequencyvz A The band pass filter 6 should have thefollowing characteristics:

Finally, f should be greater than or equal to twice f The method hereindescribed for generating quadrature information is more generallyapplicable beyond circular function transducers, with some modification,to any transducers having a characteristic function with a bounded firstderivative.

FIG. 3 illustrates schematically a laser feedback interferometer (LFI)of the type which may be obtained commercially comprising a laser mediumor cavity 11, a partially transmitting output mirror 12 at one end ofthe cavity 11, external reflector 13 outward of the cavity 11 frommirror 12, and photodetector 14 positioned outward of the cavity 11 atthe end opposite reflector 13. Such a system constitutes a circularfunction transducer in which the input, x, is a variation in the opticalpath length between the output mirror 12 and external reflector orretroreflector 13 corresponding to a variation in the parameter to bemeasured. The output from the photocell detector 14 is a substantiallysinusoidal function-of uniform variations in the parameter to bemeasured, and the output signal frequency is proportional to the rate ofchange of the parameter to be measured.

The parameter to be measured could be the distance between the outputmirror and the retro-reflector or it could be the refractive index of amedium placed between the output mirror and the retro-reflector or anyparameter which produces a corresponding variation in the optical pathlength between the output mirror and retro-reflector. In the case wherea distance or length is to be measured, the retro-reflector 13 ismounted on a suitable displacement device 9, one form of which isillustrated in FIG. 4. The displacement device includes a carriage 14mounted on a stationary base plate 15 by steel spring strips 16 and 17.The two steel strips which form the support between the translatingcarriage 14 and the stationary base plate 15 are sufficiently rigid tohold the carriage 14 without significant sagging but are flexible enoughto permit small motions of the carriage forward and backward relative tothe base plate. The two metal strips 16 and 17 constrain the carriage 14to maintain a constant angular relation with the base 15. Consequently,for small motions as are required in the instant use to which thecarriage is to be put, the motion of the carriage has essentially norotation.

To eliminate undesired vibrations the optical components and carriagemay be placed on a vibration-absorbing material. The optical system maybe isolated from air turbulence by enclosure in a transparent plasticbox or other suitable enclosure.

Mounted between the carriage and base plate by suitable insulators 18and 19 is a wire 20 whose expansion and contraction is to be measured asa result of increasing or decreasing current passing through the wire.Thus, the input x to the LFI as a circular function transducer is avariation in the distance between the output mirror and retro-reflectorcorresponding to a variation in the parameter to be measured. A suitablecarriage and displacement device upon which the retro-reflector may bemounted for more generalized spatial measurements is described in US.Pat. No. 2,604,004 issued to Root in 1952.

According to the present invention, the input x to the LFI is modulatedby a small periodic perturbation of amplitude Ax and frequency h. Themodulation may be accomplished by a variation of the index of refractionin the optical path, or a variation of the index of refraction in theoptical path, or a variation in the distance between the output mirrorand external reflector by vibrations of the output mirror, externalreflector, rear vacity mirror or the entire laser cavity. A variation ofthe index of refraction in any portion of the optical path between theoutput mirror and retro-reflector can be easily produced by theelectro-optic Pockels Effect or by actually changing the density of aregion. The Pockels Effect, whereby the index of refraction varies as alinear function of an electric field, may be utilized by inserting apotassium dihydrogen phosphate (K DP) crystal or similar material into aportion of the optical path and applying a periodic voltage to it. Thetechnique of varying the density may be achieved by placing a confinedquantity of compressible gas in the optical path and applying a periodicpressure.

In the present illustration modulation of the input is accomplished byvarying the distance between the output mirror and retro-reflector byvibrating the retro-reflector in the direction of the optical path andat a predetermined modulating frequency. To accomplish this a quartzcrystal 22 with vapor-deposited gold faces 23 and 24 is mounted on thedisplacement device with the gold surfaces normal to the optical path.The gold surface 23 which is not attached to the displacement deviceserves as the retroreflector for the LFI. As illustrated in the blockdiagram in FIG. 3, the desired periodic variation of the optical pathlength is produced by applying the output of an audio oscillator 3' tothe two gold faces 23 and 24 of quartz crystal 22. The application of aperiodic voltage to the two faces causes a periodic contraction andexpansion of the crystal in the direction of the optical path. Goldsurface 24 is firmly attached to the massive carriage of thedisplacement device and the other surface 23 is free to oscillate. Thecrystals contraction and expansion at the predetermined modulatingfrequency f and amplitude Ax causes the retro-reflector to moveperiodically along the optically along the optical path of the LFI. Thequartz crystal thus serves the purpose of the linear transducer shown inFIG. 1. The variations in the optical path length appear in the laser aschanges in light intensity transformed to frequency components in theoutput of the photocell detector.

The output from the photocell detector is coupled to a band pass filter6 and first low pass filter of characteristics already described.Namely, the low pass filter 5 has an upper cutoff frequency at themaximum frequency f of the original output produced by variations in theparameter to be measured. The band pass filter centers around themodulating frequency f with a lower cutoff frequency less thanapproximately f f and an upper cutoff frequency greater thanapproximately f +f in order to preserve the quadrature information inthe amplitude function of the f frequency component.

The output of the band pass filter 6 to coupled to a mixer or multiplier7 which multiplies the f frequency component with the output of theaudio oscillator 3'. The audio oscillator signal must be in phase withthe f frequency component and if it is not, a suitable phase shifter canbe incorporated between the audio oscillator and multiplier. The outputof the mixer is the sum and difference of the frequencies in the inputs.Thus, the amplitude of the f frequency component appears as identicalamplitudes on a zero frequency or DC signal and a signal at 2h. Thesecond low pass filter 8 at the mixer output having an upper cutofffrequency at approximately f passes the portion of the mixer output nearzero frequency. The amplitude function is thereby extracted to produce asignal in quadrature with the original output signal obtained from thefirst low pass filter. The characteristics of the band pass filter 6 andthe low pass filters 5 and 8 are chosen to meet the conditions alreadydiscussed and illustrated in FIG. 5.

Demodulation and detection of the amplitude function of the f frequencycomponent which contains the quadrature information may be carried outby a commercial lock-in amplifier which includes as components the bandpass filter, mixer, low pass filter and phase shifter necessary forprocessing the quadrature information.

The quadrature signal and the original signal obtained from the two lowpass filters may be fed into a dual channel chart recorder tographically present the signals as illustrated in FIG. 6. In theexperimental result illustrated in FIG. 6, the wire 20 was first heatedso that the distance between the output mirror and retro-reflector wasdecreasing prior to A. During that time the quadrature signal wasleading the original signal by 90. At A, upon cooling the wire, thedistance began increasing, and although the change of direction is notapparent in the original signal, it is indicated in the quadraturesignal which then lags behind the original signal by 90. At point B thedirection of the carriage was reversed a second time and again thechange in direction is apparent from the quadrature signal. Thequadrature signal again leads the original signal by 90 A third reversalat point C is apparent in the original signal but not in the quadraturesignal. Thus, the quadrature signal and original signal in combinationat all points provide the necessary directional information to resolveany ambiguity in the output.

Alternatively, the original signal and quadrature signal may beconnected separately to the vertical and horizontal deflection plates ofan oscilloscope to obtain an ellipse or circle and the directionalinformation obtained from the direction of rotation of the oscilloscopespot.

As shown in a portion of FIG. 7, the original signal and quadraturesignal could also be connected to the inputs of and up-down orreversible counter 64 through suitable Wave form shaping circuits 61 and62 and a directional logic circuit 63 to obtain addition of cyclesproduced by variation of the parameter to be measured in one directionand subtraction of cycles produced by variation or motion of theparameter to be measured in the opposite direction. The output of theup-down counter may then be recorded or displayed at 67. Such circuitsfor wave form shaping, directional logic, and up-down or reversiblecounting and recording are well known and are described in US. Pat. No.2,604,004 issued to Root in 1952 and in an article by Peck and Obetz invol. 43, No. 6, of the Journal of the Optical Society of America, p.505, 1953.

In the circuitry and apparatus described, amplifiers may be necessary atvarious points such as at the output of the photocell detector,depending upon the equipment used.

The quadrature technique heretofore described can also be used toprovide compensation information in interferometers in order to correctfor variations in the index refraction of the ambient atmosphere therebypermitting greater accuracy and higher resolution. As applied to the LPIillustrated in FIG. 8, a beam splitter 25 is placed in the optical pathbetween the laser output mirror and retro-reflector. The beam splitterdeflects a portion of the laser beam to a second retroreflector 26. Todetect and compensate for variations in the atmospheric conditions, thephysical length of the deflected compensation beam must be held constantby extremely low coefficient of expansion materials, such as Invar.

According to this aspect of the invention, a second piezoelectriccrystal such as a quartz crystal 30 with gold surfaces 31 and 32 ismounted on the material 33 of low coefficient of expansion which definesthe deflected compensation beam path length. Gold surface 32 is normalto the deflected compensation beam path and acts as the second externalreflector or retro-reflector. Variations in the refractive index of theambient atmosphere produces a corresponding variation in the opticalpath length of the deflected compensation beam thereby producin a directsignal in the photocell, output which is a sinusoidal function of thevariation in the refractive index of the ambient atmosphere whosefrequency is proportional to the rate of change of the refractive index.

As in the quadrature technique already described, the deflectedcompensation beam is modulated to provide directional information as tothe variations in the ambient atmosphere. To this end a second audiooscillator 43 applies a small periodic voltage to the gold surfaces ofsecond quartz crystal 30 of frequency f thereby providing a periodicvariation in the optical path length of the deflected compensation beamthereby modulating the beam at the predetermined modulating frequency fThe components utilized in parameter measurement are the same as in FIG.3 heretofore described. The LFI output G(y, t) attributable to thevariations of the refractive index in the ambient atmosphere and thecompensation beam modulation at frequency f; is given by the followingequation where y is the refractive index times the compensation pathlength, Ay is the amplitude of the compensation beam modulating signal,X is half the operating wavelength of the laser, and B is a scalefactor, proportgional to the amount of feedback in the compensation eam.

Eu a) in X S Gfy, t) =BJ 1% cos [Equation 5Continued, col. 9]

21rAy cos 27mm] E Re [ZBe X [Equation A e, owe, o+ o 3,") c0 2 2 +BJ 3?cos-: 2

21113112 2AJ1 Sln -2BJ sin 21rAy X 21ry X cos 2rrf t [Equation 6] Thefrequency component f due to changes in the index of refraction of theambient atmosphere is of a long period and, therefore, in the frequencyrange of the original output produced by variations of the parameter tobe measured. In order to avoid interference between f and f,,,, the fcomponent in the laser output may be initially eliminated andinformation as to f obtained from the amplitude function of a higherfrequency component in the output. Thus the term BJ 32 cos may beeliminated by making Ay such that 27rAy X is a root of the zero orderBessel function I This eliminates the third term to the right of thesign in Equation NO. 6, and information as to f component must beobtained from the sixth term of Equation No. 6 where it is contained inthe amplitude function of the 2 frequency component. Thus, the secondand fourth terms of the Equation No. 6 contains the parametermeasurement beam information while the fifth and sixth terms of theEquation No. 6 contain the index of refraction compensation beaminformation.

The parameter measurement beam information obtained in the f andfrequency components of the LEI output are processed as illustrated inFIG. 3 heretofore described to obtain an original signal and the signalin quadrature therewith which provide measurement information of theparameter to be measured.

The f and 2 frequency components of the LEI output which contain thecompensation beam information are processed as follows. The 2 frequencycomponent has as an amplitude function the original f informationattributable to variations in the refractive index of the ambientatmosphere. Thus, the 2 frequency component is separated by a secondband pass filter 46 having a frequency range of approximately 2f --f to213+ in order to preserve the direct signal information of the frequencycomponent f produced by variations in the ambient at mosphere. Theoutput from this second band pass filter 46 is put into a mixer ormultiplier 47 where it is multiplied by the output of the second audiooscillator 43 which has been passed through a frequency doubler 49.Thus, the frequency component 2 is multiplied by a signal of the samefrequency and the same phase. If there is any phase difference betweenthese signals, a phase shifter can be utilized to maintain the signalsin phase. The output from this second mixer or multiplier 47 is putthrough a low pass filter 48 with an upper cutoff frequency ofapproximately f to thereby extract the direct signal corresponding tothe amplitude function of frequency f produced by variations in therefractive index of the ambient atmosphere.

The f frequency component Which contains as its amplitude function thequadrature information for the direct signal of frequency f is separatedfrom the LEI output by a third band pass filter 56 of frequency rangefrom f f to f +f in order to preserve the quadrature information. Theoutput from this third band pass filter 56 is fed to a third mixer ormultiplier 57 and multiplied with the output of the second audiooscillator 43 which produces a signal of the same frequency and phase.The output from this third mixer 57 is put into a third loW pass filter58 with an upper cutoff frequency f to thereby obtain a signal inquadrature with the direct signal produced by variations in therefractive index of the ambient atmosphere.

As illustrated in FIG. 9, the first band pass filter 6 has a frequencyrange of approximately that indicated by band 6. The second band passfilter 46 has a frequency range of approximately that indicated by band46'. The

third band pass filter 56 has a frequency range of approximately thatindicated by band 56. The first low pass filter 8 has a frequency rangeapproximately that indicated by band 8'. The frequency :bands indicatedon the graph in FIG. 10 indicate the ranges selected to avoid overlapand thereby permit simple filtering in order to separate out thefrequency components from the LEI output.

Analysis of Equation No. 5 indicates that in order to preclude overlapbetween the measurement information frequency components and thecompensation information frequency components in the various frequencydomains, the following restrictions on f f f and f should be observedwhere f is less than /2 f This permits separation of each of the foursignals as illustrated in the graph in FIG. 9. If these restrictions onthe frequencies are observed, the following frequency ranges areavailable for the band pass filters. For the first band pass filter 6,

f +f upper cutoff frequency 2f -j For the second band pass filter 46,

f +f lower cutoff frequency 2f f Zf +f upper cutoff frequency For thethird band pass filter 56,

f lower cutoff frequency f -f fz+fc pp cutoff q y f1fm As shown in FIG.10, the direct signal output and its quadrature containing thecompensation information may be passed respectively through second Waveform shaping circuits 71 and 72 and then together through a directionallogic circuit 73 and up-down or reversible counter 74. The output ofthis second reversible counter may then be processed through a scalefactor calculator 75 to a digital multiplier 76 with the output from thefirst reversible counter thereby appropriately to adiust the measurementinformation from the first reversible counter to compensate forvariations in the refractive index of the ambient 1 1 atmosphere forsubsequent display 77. Such circuitry is well known and need not bedescribed here.

The degree of resolution of the apparatus described herein is in itssimplest form one-half the wave length of the operating frequency of theLFI. This resolution is obtained from the original and quadrature signalalone. A small increase in the electronic logic can increase theresolution to one-eighth the wave length of the laser frequency and evenmore by utilizing an angle resolver 78 to resolve the angle of thesinusoidal output between peaks. Such an angle resolver 78 might beeither a servomechanism resolver or a sine-cosine resolver as used inmodern analog computers and well known in the art. Such an angleresolver 78 is shown in the data processing diagrams illustrated inFIGS. 7 and 10.

If the index of refraction compensation is not required, thecompensation beam can be used as a second measurement beam in which thepath length is allowed to vary. This makes possible two LFIs from thesame laser provided that the restrictions on the frequency ranges of fand f heretofore described are followed. The method for this variationis the same as described in the compensation technique with the secondexternal reflector 30 mounted for instance on a suitable displacementcarriage for motion in response to a second parameter to be measured.

The LFI described herein is particularly well adapted for applicationsin fields such as strain seismometry, machine tool screw calibration,machine tool position control, the precision positioning of masks in themanufacture of integrated circuits, etc.

While two embodiments of this invention have been shown and described,it will be apparent that other adaptations and modifications can be madewithout departing from the true spirit and scope of the invention.

What is claimed is:

1. Apparatus for generating a compensation signal in interferometers ofthe type having first and second reflector means and a light sourceproviding a beam of light reflected therebetween and wherein the inputis a variation in the optical pathlength between the first reflector andsecond reflector means corresponding to a variation in a parameter to bemeasured and the interferometer output is a substantially circularfunction of the input comprising:

a beam splitter interposed between the first and second reflector meansto deflect a portion of the beam away from said second reflector means;

a third reflector means interposed in the path of said deflected beamwhereby said deflected beam detects changes in the refractive index ofthe ambient atmosphere thereby producing a direct signal output from theinterferometer of frequency f proportional to the rate of change in therefractive index of the ambient atmosphere; means for modulating thedeflected beam at a predetermined modulating frequency 3;

means at the interferometer output for separating the direct signalfrequency component of frequency f produced by the rate of change of therefractive index of the ambient atmosphere and the modulating frequencycomponent of frequency f means for demodulating the modulating frequencycomponent to obtain a signal in quadrature with said direct signalproduced by the change in the refractive index of the ambientatmosphere.

2. Apparatus for generating a quadrature signal and a compensationsignal in interferometers of the type having first and second reflectormeans and a light providing a light beam reflected therebetween andwherein the input is a variation in the optical pathlength between thefirst and second reflector means corresponding to a variation in aparameter to be measured and the output from the interferometer is asubstantially circular function of the input for uniform changes in theparameter to be meas- 12 ured, said output frequency being proportionalto the rate of change of the parameter to be measured and having amaximum frequency value f due to the maximum rate of change of theparameter to be measured comprising:

first modulating means for modulating the input by a perturbation offrequency h;

a. beam splitter interposed between the first and second reflector meansto deflect a portion of the inter ferometeibeam away from said secondreflector means;

a third reflector means interposed in the path of said deflected beamwhereby said deflected beam detects changes in the refractive index ofthe ambient atmosphere thereby producing a direct signal output from theinterferometer of frequency f proportional to the rate of change in therefractive index of the ambient atmosphere;

second modulating means for modulating the deflected beam by aperturbiation of frequency f said frequency f f f and f satisfying thefollowing conditions:

first low pass filter coupled with the interferometer output whereby theoriginal output frequency component of maximum frequency f produced bythe change in the parameter to be measured is separated, said first lowpass filter having the following characteristic approximately:

first band pass filter coupled with the interferometer output whereby afrequency band at f is separated, said first band pass filter having thefollowing characteristics approximately:

f +f lower cutoff frequency f ;f f +f upper cutoff frequency 2f -f firstdemodulating means coupled with the output from said first band passfilter whereby a signal in quadrature with said original output signalof maximum frequency f is produced;

second band pass filter coupled with the interferometer output whereby afrequency band at 2 is separated, said second band pass filter havingthe following characteristics approximately:

f +f lower cutoff frequency 2) f 2f +f upper cutoff frequency seconddemodulating means coupled with the output of said second band passfilter whereby the direct signal of frequency i is produced byvariations in the refractive index of the ambient atmosphere isobtained;

third band pass filter coupled with the interferometer output whereby afrequency band at f is separated, said third band pass filter having thefollowing characteristics approximately:

f lower cutoff frequency f f third demodulating means coupled with theoutput of said third band pass filter whereby a signal in quadraturewith said direct signal of frequency f produced by variations in therefractive index of the ambient atmosphere is obtained.

3. Apparatus for generating a quadrature signal and a compensationsignal in interferometers as set forth in claim 2 wherein said firstdemodulating means comprises a first mixer coupled to the output of saidfirst band 13 pass filter multiplying the output with a signal of thesame phase and same frequency and a second low pass filter coupled tothe output of said first mixer and having an upper cutoff frequency ofapproximately f and wherein said second demodulating means comprises asecond mixer coupled to the output of said second band pass filtermultiplying the output with a signal of the same phase and samefrequency and a third low pass filter coupled to the output of saidsecond mixer and having an upper cutolf frequency of approximately f andwherein said third demodulating means comprises a third mixer coupled tothe output of said third band pass filter multiplying the output with asignal of the same phase and same frequency and a fourth low pass filtercoupled to the output of said third mixer and having an upper cutoiffrequency of approximately f 4. Apparatus for generating a quadraturesignal and a compensation signal in interferometers as set forth inclaim 2 further provided with:

first wave form shaper means, first directional logic means and firstup-down counter means into which are coupled the original output signalproduced by variations in the parameter to be measured and the signal inquadrature therewith whereby variations of the parameter in onedirection are added and variations in another direction are substracted;

second wave form shaper means, second directional logic means and secondup-down counter into which are coupled the direct signal produced byvariations in the refractive index of the ambient atmosphere and thesignal in quadrature therewith whereby variations in the refractiveindex in one direction are added and variations in another direction aresubtracted;

and scale factor calculator means into which is coupled the output fromsaid second up-down counter whereby a signal corresponding to the ratioof current index of refraction to that when the interferometer was lastcalibrated is produced;

and digital multiplier means into which is fed the output from the firstup-down counter and the output from the scale factor calculator toproduce the corrected measurement signal. 5;. Apparatus as set forth inclaim 2 wherein: said first modulating means comprises a firstpiezoelectric crystal upon which the second reflector means is mountedand first oscillator means for applying a periodic voltage across thecrystal to thereby cause periodic contraction and expansion of thecrystal in a direction normal to the face of the second reflector meansat a predetermined modulating frequency f and wherein said secondmodulating means comprises a second piezoelectric crystal upon which thethird reflector means is mounted and second oscillator means forapplying a periodic voltage across the crystal to thereby cause periodiccontraction and expansion of the crystal in a direction normal to theface of the third reflector means at a predetermined modulatingfrequency f 6. Apparatus for generating a quadrature signal and acompensation signal in interferometers as set forth in claim 2 whereinthe amplitude AY of the perturbation from said second modulating meanssatisfies the condition that 21rAY X of the type having a laser medium,output mirror, first external reflecotr, and photocell detector andmeans for varying the optical pathlength between the output mirror andfirst external reflector in response to a variation in a first parameterto be measured, wherein the input due to a variation in the firstparameter to be measured is a variation in the optical pathlengthbetween the output mirror and first external reflector and wherein theoutput from the photocell detector is a substantially circular functionof the input, the frequency of said output component due to a change inthe first parameter being proportional to the rate of change of thefirst parameter to be measured and having a maximum value f comprising:

first modulating means for modulating the input by a perturbation offrequency h;

a beam splitter interposed between the first output mirror and firstexternal reflector to deflect a portion of the interferometer beam awayfrom said first external reflector;

a second external reflector interposed in the path of said deflectedbeam;

means for varying the optical pathlength between said beam splitter andsaid second external reflector in response to variations in a secondparameter to be measuredthereby producing a direct signal component inthe output of the interferometer of frequency proportional to the rateof change of a second parameter to be measured having a maximum value offrequency fc;

second modulating means for modulating the deflected beam by aperturbation of frequency f said frequencies f f f and f satisfying thefollowing conditons: fm fc i12 (fm+fc) first low pass filter coupledwith the photocell detector output whereby the orignal ouput frequencycomponent of maximum frequency f produced by the change in the firstparameter to be measured is separated, said first low pass filter havingthe following characteristic approximately:

first band pass filter coupled with the photocell detector outputwhereby a frequency band at f is separated, said first band pass filterhaving the following characteristics approximately:

f +f lower cutoff frequency f f h f upper cutoff frequency 2f -f firstdemodulating means coupled with the output from said first band passfilter whereby a signal in quadrature with said original output signalof maximum frequency f is produced;

second band pass filter coupled with the photocell detector outputwhereby a frequency band at 21 is separated, said second band passfitler having the following characteristics approximately:

f f lower cutoff frequency 2 g, f 2 f f upp er cutoff frequency seconddemodulating means coupled with the output of said second band passfilter whereby the direct signal of frequency f produced by 'variationsin the second parameter to be measured is obtained;

third band pass filter coupled with the photocell detector outputwhereby a frequency band at f is separated, said third band pass filterhaving the following characteristics approximately:

third demodulating means coupled with the output of said third band passfilter whereby a signal in quadrature with said direct signal offrequency f produced by variations in the second parameter to bemeasured is obtained.

8. Apparatus for simultaneously measuring two parameters in combinationwith a laser feedback interferrometer as set forth in claim 7 whereinthe amplitude AY of the perturbation from said second modulating meanssatisfies the condition that is a root of the zero order Bessel functionof the first kind, where X is one-half the operating wave length of thelaser.

9. Apparatus for generating a quadrature signal in laser feedbackinterferometers comprising:

a laser feedback interferometer comprising a laser meddium, laser outputmirror, external retrorefiector in the laser output path, andphotodetector for detecting the laser output, all along a common axiswherein the interferometer input is a change in the optical pathlengthbetween the output mirror and external retroflector in proportion to achange in a parameter to be measured and wherein the output is derivedfrom the photodetector;

means for modulating the input by a perturbation of frequency, 11, atleast equal to twice the maximum frequency, f of the original outputproduced by the rate of change in the parameter to be measured;

means at the output of the transducer for separating the modulatingfrequency component of the output from the original frequency componentof the output produced by the rate of change in the parameter to bemeasured comprising a first low pass filter coupled with the transduceroutput having the following characteristic approximately:

f cutotf frequency /2 f and a band pass filter coupled with thetransducer output and in parallel with said first low pass filter andhaving the following characteristics approximately:

/2 f glower cutoff frequency f f f +f upper cutoff frequency y f meansfor demodulating the modulating frequency component after separationfrom the original output component comprising a mixer coupled with theoutput of said band pass filter wherein the modulating frequencycomponent is multiplied with an unmodulated signal of the same frequencyand same phase to produce carriers of approximately zero frequency andapproximately twice the modulating frequency respectively having thesame amplitude as the modulating frequency component; and a second lowpass filter coupled with the mixer output having the followingcharacteristic approximately:

f cutoff frequencyVzf thereby to produce a signal corersponding to theamplitude function of the modulating frequency component and inquadrature with the original output signal. 10. Apparatus for generatinga quadrature signal for circular function transducers as set forth inclaim 9 wherein there is also provided in sequence, wave form shapingmeans, directional logic means and an up-down counter and to which theoriginal output signal and quadrature signal are fed whereby cycles inthe original output signal are added for variation of the parameter tobe measured in one direction and subtracted for variation of theparameter to be measured in another direction.

References Cited UNITED STATES PATENTS 3,409,370 11/1968 King et al33194.5 3,409,375 11/1968 Hubbard 356-106 RONALD L. WIBERT, PrimaryExaminer C. CLARK, Assistant Examiner US. Cl. X.R. 331-94.5

